Eyes in the sky, courtesy of Dundee Satellite Receiving Station bring this image of a spiral depression near Greenland.
Such perfectly represented spiral lows happen when the vortex is present through all layers of the atmosphere: surface streamlines as well as wind aloft trace out the same pattern circular pattern. This is often not the case in the mid-latitudes. See following images from Earthnullschool which show that the surface low is located at the same position as the upper low.
The trailing cold front has a marked wind veer on it.
UKMO analysis for same day follows, which shows the somewhat complicated structure of the frontal system. Bands of airflow are sucked up from the south and gradually wind upwards and around the vortex thereby mixing warm northwards. There is a noticeable change in air mass because behind the front we can see convective cells in the polar airflow which pours down from the Davis Straits between Greenland and Canada.
Spirals, and in particular logarithmic spirals often occur in nature. The dynamics are complicated here so there is no simple equation; circular motion on the surface of a spinning sphere moving in an elliptical orbit. There seems to be an undeniable approximation to the following.